Answer to Question #52685 in Linear Algebra for ravish

Question

a)Consider the funtion f:R\{−1}→R defined by f(x)=2x+1 x+1. i) ii) iii) iv) Check that f(x) is well defined and 1−1. Check that f(x)=2 for any x∈R. Check that g:R\{2}→R given by g(x)=x−1 Further,check that g(x)=−1 for any x∈R. 2−x is well defined and 1−1. (20) (3) (2) (4) Check that (f◦g)(x)=x for x∈R\{2} and (g◦f)(x)=x for x∈R\{−1}.(4) b)Find the direction cosines of the perpendicular from the origin to the plane r·(6i+4j+2√ 3k)+2=0.